Highly efficient optical gratings with reduced thickness requirements and impedance-matching layers

ABSTRACT

An optical grating comprising a grating layer and two surface layers, the layers being arranged with the grating layer between the surface layers. The grating layer comprises a set of multiple, discrete, elongated first grating regions that comprise a first dielectric material and are arranged with intervening elongated second grating regions. The bulk refractive index of the dielectric material of the first grating regions is larger than the bulk refractive index of the second grating regions. The first surface layer comprises a first impedance matching layer, and the second surface layer comprises either (i) a second impedance matching layer or (ii) a reflective layer. Each said impedance matching layer is arranged to reduce reflection of an optical signal transmitted through the corresponding surface of the grating layer, relative to reflection of the optical signal in the absence of said impedance matching layer.

BENEFIT CLAIMS TO RELATED APPLICATIONS

This application is a divisional of U.S. non-provisional applicationSer. No. 12/265,721 filed Nov. 5, 2008 now U.S. Pat. No. 8,165,436,which claims benefit of: (i) U.S. provisional App. No. 61/002,059 filedNov. 5, 2007; (ii) U.S. provisional App. No. 61/005,647 filed Dec. 5,2007; (iii) U.S. provisional App. No. 61/011,589 filed Jan. 18, 2008;(iv) U.S. provisional App. No. 61/068,544 filed Mar. 6, 2008; and (v)U.S. provisional App. No. 61/126,757 filed May 6, 2008. Each of saidapplications is hereby incorporated by reference as if fully set forthherein.

BACKGROUND

The field of the present invention relates to optical gratings. Inparticular, highly efficient optical gratings are disclosed herein thatinclude at least one impedance matching layer or are arranged to exhibitreduced polarization dependence.

A wide variety of optical gratings are available for diffracting opticalsignals, in transmission or in reflection. One particular example isdisclosed by Wang et al (“Deep-etched high-density fused-silicatransmission gratings with high efficiency at a wavelength of 1550 nm,”Applied Optics, Vol 45 No 12 p 2567 (2006)). The optical gratingdisclosed therein comprises relatively deep etched grooves in a fusedsilica substrate (about 2.5 μm deep for maximum diffraction efficiencyat 1550 nm). The optical gratings disclosed by Wang et al can beadvantageously employed, for example, for dividing or combining opticalsignals of differing wavelengths in a dense wavelength divisionmultiplexing (DWDM) optical telecommunications system.

It is desirable to provide efficient gratings with reduced thickness(i.e., etch depth) requirements. While the optical gratings disclosed byWang et al can be highly efficient (calculated >95%, measured >87% forTE polarization), it is nevertheless desirable to provide opticalgratings that exhibit increased efficiency, decreased polarizationdependence, or decreased wavelength dependence. Such improved opticalgratings would find wider applicability in a variety oftelecommunications or other optical implementations.

SUMMARY

An optical grating comprising a grating layer and two surface layers,the layers being arranged with the grating layer between the surfacelayers. The grating layer comprises a set of multiple, discrete,elongated first grating regions that comprise a first dielectricmaterial and are arranged with intervening elongated second gratingregions. The bulk refractive index of the dielectric material of thefirst grating regions is larger than the bulk refractive index of thesecond grating regions. The first surface layer comprises a firstimpedance matching layer, and the second surface layer comprises either(i) a second impedance matching layer or (ii) a reflective layer. Eachsaid impedance matching layer is arranged to reduce reflection of anoptical signal transmitted through the corresponding surface of thegrating layer, relative to reflection of the optical signal in theabsence of said impedance matching layer.

Objects and advantages pertaining to optical gratings may becomeapparent upon referring to the exemplary embodiments illustrated in thedrawings and disclosed in the following written description or appendedclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic plan view of an exemplary optical grating layer.FIG. 1B is a schematic cross sectional view of the exemplary opticalgrating layer arranged as a transmission grating. FIG. 1C is a schematiccross sectional view of the exemplary optical grating layer arrangedwith a reflecting layer as a reflection grating.

FIGS. 2A and 2B illustrate schematically low-index and high indexoptical modes, respectively, that propagate through an exemplary gratinglayer.

FIG. 3 is a calculated plot of optimal grating depth versus refractiveindex difference between regions of a grating layer of an exemplaryoptical transmission grating.

FIG. 4A is a schematic cross-sectional view of an exemplary opticaltransmission grating layer; FIG. 4D is a calculated plot of thecorresponding diffraction efficiency versus grating layer thickness.FIG. 4B is a schematic cross-sectional view of an exemplary opticaltransmission grating layer with one impedance matching layer; FIG. 4E isa calculated plot of the corresponding diffraction efficiency versusgrating layer thickness. FIG. 4C is a schematic cross-sectional view ofan exemplary optical transmission grating layer with two impedancematching layers; FIG. 4F is a calculated plot of the correspondingdiffraction efficiency versus grating layer thickness.

FIGS. 5A and 5B illustrate schematically assembly of an exemplaryoptical grating layer and an impedance matching layer.

FIG. 6 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIG. 7 is a calculated plot of diffraction efficiency and polarizationdependent loss (PDL) versus wavelength for one arrangement of theexemplary optical grating of FIG. 6.

FIGS. 8A and 8B are calculated plots of diffraction efficiency andpolarization dependent loss (PDL) versus wavelength for alternativearrangements of the exemplary optical grating of FIG. 6.

FIG. 9 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIG. 10 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIGS. 11A and 11B are each schematic cross-sectional views of exemplaryoptical transmission gratings with impedance matching layers.

FIG. 12 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIGS. 13A and 13B are each schematic cross-sectional view of exemplaryoptical transmission gratings with impedance matching layers.

FIG. 14 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIG. 15 is a calculated plot of diffraction efficiency and polarizationdependent loss (PDL) versus wavelength for one arrangement of theexemplary optical grating of FIG. 14.

FIG. 16 is a calculated plot of diffraction efficiency and polarizationdependent loss (PDL) versus wavelength for alternative arrangements ofthe exemplary optical grating of FIG. 14.

FIG. 17 is a table illustrating the dependence of grating performance onfabrication tolerances for the exemplary optical grating of FIG. 14.

FIG. 18 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIG. 19 is a calculated plot of diffraction efficiency and polarizationdependent loss (PDL) versus wavelength for the exemplary optical gratingof FIG. 19.

FIG. 20 is a table illustrating the dependence of grating performance onfabrication tolerances for the exemplary optical grating of FIG. 18.

FIG. 21 is a schematic cross-sectional view of an exemplary opticaltransmission grating with impedance matching layers.

FIG. 22 is a schematic cross-sectional view of an exemplary opticalreflection grating with an impedance matching layer.

FIG. 23 is a calculated plot of diffraction efficiency and polarizationdependent loss (PDL) versus wavelength for the exemplary optical gratingof FIG. 22.

FIG. 24 is a schematic cross-sectional view of an exemplary opticalreflection grating with an impedance matching layer.

FIG. 25A is a calculated plot of diffraction efficiency versuswavelength for the exemplary optical grating of FIG. 24. FIG. 25B is acalculated plot of diffraction efficiency versus incident angle for theexemplary optical grating of FIG. 24.

FIGS. 26A-C are calculated plots of diffraction efficiency versusgrating layer thickness for differing incident and diffracted angles foran exemplary optical grating.

FIGS. 27A and 27B are calculated plots of diffraction efficiency versusgrating layer thickness for differing polarizations for an exemplaryoptical grating. FIG. 27C is a calculated plot of diffraction efficiencyversus wavelength for an exemplary optical grating.

FIG. 28 is a schematic cross-sectional view of an exemplary opticalreflection grating with an impedance matching layer.

FIG. 29 is a schematic cross-sectional view of an exemplary opticalreflection grating with an impedance matching layer.

FIG. 30 illustrates schematically assembly of an exemplary opticalgrating layer and a reflecting layer.

FIGS. 31A-31D are schematic cross-sectional views of exemplary opticalgratings with impedance matching layers.

FIG. 32A is a schematic cross-sectional view of an exemplary opticalgrating with impedance matching layers. FIG. 32B is a calculated plot ofdiffraction efficiency versus grating layer thickness for the exemplaryoptical grating of FIG. 32A.

FIGS. 33A and 33B illustrate schematically exemplary opticalinterference patterns calculated in a grating layer.

FIG. 34 is a schematic plan view of an exemplary optical grating layerarranged according to a calculated interference pattern.

It should be noted that the embodiments depicted in this disclosure areonly shown schematically, and that not all the features may be shown infull detail or in proper proportion. Certain features or structures maybe exaggerated relative to others for clarity. For example, the actualoptical gratings depicted as having a handful of diffractive lines ofridges typical have hundreds or thousands of lines per millimeter. Thenumber of lines is reduced in the drawings for clarity. It should benoted further that the embodiments shown are exemplary only, and shouldnot be construed as specifically limiting the scope of the writtendescription. It is intended that equivalents of the disclosed exemplaryembodiments and methods shall fall within the scope of the presentdisclosure. It is intended that the disclosed exemplary embodiment, andequivalents thereof, may be modified while remaining within the scope ofthe present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

FIG. 1A is a schematic plan view of an exemplary grating layer 100arranged in the xy-plane. Grating layer 100 comprises a set of multiple,discrete, elongated first grating regions 101 (i.e., the grating “lines”that run along the y-direction). The grating regions 101 comprise afirst dielectric material of bulk index n_(hi). The grating regions 101,or equivalently grating lines 101, are arranged with interveningelongated second grating regions 102 (i.e., the “spaces” between gratinglines 101) having a bulk refractive index n_(lo) that is lower thann_(hi). The second grating regions 102 can be empty space or can befilled with air or other ambient atmosphere or inert gas (in which casen_(lo) would be about equal to unity). Alternatively, the second gratingregions 102 can comprise a second dielectric material filling the spacesbetween the first grating regions 101. FIG. 1B is a schematic crosssectional view of grating layer 100 arranged as a transmission grating,while FIG. 1C is a schematic cross sectional view of grating layer 100arranged as a reflection grating (with reflecting layer 103). Thegrating period (equivalently, the grating spacing) is Λ, the gratinglayer thickness is d, the width of the grating regions 101 is b, and thegrating duty cycle is f=b/Λ. The grating wavevector is parallel to thex-direction. All of those grating parameters are defined locally, andcan be constant over the entire grating layer 100 or can vary over thearea of the grating layer 100. While the grating layer 100 has beencharacterized as being flat for convenience of the present disclosure,the principles disclosed can be generalized to curved grating layers aswell.

As is well known, an optical signal at a wavelength λ that is incidenton the grating layer 100 having grating period Λ can be diffracted intoone or more transmitted diffracted orders according to the gratingequation: n_(A) sin θ_(in)+n_(S) sin θ_(d,m)=mλ/Λ, where m designatesthe diffracted order (zero, ±1, ±2, and so on), θ_(in) is the incidenceangle (relative to the grating-normal vector), θ_(d,m) is the diffractedangle (relative to the grating-normal vector) for the mth diffractedorder, and n_(A) and n_(S) are the refractive indices of ambient andsubstrate media, respectively. Simple transmission (refraction)satisfies the grating equation for m=0 (zeroth order); non-zero-orderdiffracted orders are those that satisfy the grating equation for m≠0.

To maximize diffraction efficiency into only one diffracted order, Λ istypically chosen to be comparable to or shorter than the wavelength λ ofan optical signal incident on the grating layer, thereby limitingdiffraction to only the first diffracted order. If the presence ofmultiple diffracted orders is acceptable, then larger grating periodscan be employed. All of the dielectric materials employed aresubstantially transparent over at least a selected operationalwavelength range. The operational wavelength range is typically in thevisible or near infrared spectral range, although other spectral regionscan be employed. Particular wavelength ranges of interest are 1525-1565nm (ITU telecom C-band) and 1570-1620 nm (ITU telecom L-band), which areused in DWDM optical telecommunications systems. Any other selectedoperational wavelength range shall fall within the scope of the presentdisclosure or appended claims.

In FIG. 1B, the grating layer 100 is arranged as a transmission gratingsurrounded by air or other inert gas as adjacent materials. Thoseadjacent materials can be referred to as substrate or superstratematerials. Often a substrate other than air is employed for mechanicalsupport during fabrication or use of the transmission grating. Suitablesubstrate materials include but are not limited to fused silica,borosilicate glass, borophosphate glass, soda lime glass, or polymer. Asubstrate material can also be employed as the dielectric materialfilling the second grating regions; a polymer may be particularly wellsuited for that purpose. Any substrate material used for a transmissiongrating must be substantially transparent over the operation wavelengthrange.

In FIG. 1B, an optical signal with wavevector k_(in) is incident on thegrating layer 100. In this example the optical signal's incident angleθ_(in) (with respect to the grating layer normal) is chosen so that themagnitude of the incident signal's wavevector component along the x-axisis about equal to half of the grating wavevector magnitude. Thatgeometry results in a reflected diffracted wave with wavevector k_(r-1)that is collinear but anti-parallel with the input signal (reflectednegative first order diffracted signal), and a transmitted diffractedwave with wavevector k_(t-1) (transmitted negative first orderdiffracted signal) that propagates at an angle θ_(d) with respect to thegrating layer normal, where θ_(in)≈θ_(d). Wavevectors k_(r0) and k_(t0)denote the specularly reflected and directly transmitted signals (zerothorder diffracted signals).

The diffraction efficiency of the transmitted negative first orderdiffracted signal depends on the thickness d of the grating as well asthe bulk refractive indices n_(hi) and n_(lo) of the first and secondgrating regions 101 and 102, respectively. For appropriately chosengrating thickness and refractive indices, greater than 90% of theincident optical signal can be diffracted into the first transmitteddiffracted order. Additionally, the duty cycle of the grating can beoptimized along with the bulk indices and thickness to reduce thepolarization-dependence of the diffraction efficiency into the firstdiffracted order, as described further below.

The grating layer 100 of FIG. 1B can be characterized as a periodic slabwaveguide, and the optical signal incident on the grating layer 100couples into bound optical modes that propagate through the gratinglayer 100 in the z-direction. The electric field amplitudes of the twobound grating modes of interest are depicted in FIGS. 2A and 2B. In FIG.2A, a first (or “fast”) grating mode 201 has a periodically varyingfield amplitude with its intensity substantially confined to the lowrefractive index regions of the grating, i.e., electric field maxima arelocated within regions of refractive index n_(lo) and electric fieldnodes are located within regions of refractive index n_(hi). In FIG. 2B,a second (or “slow”) grating mode 202 is shown that has a periodicallyvarying field amplitude with its intensity substantially confined to thehigh refractive index regions of the grating, i.e., electric fieldmaxima are located within regions of refractive index n_(hi) andelectric field nodes are located within regions of refractive indexn_(lo). The “slow” grating mode propagates with a phase velocity that isclose to c/n_(hi) (modal index close to n_(hi)), and the “fast” gratingmode propagates with a phase velocity that is close to c/n_(lo) (modalindex close to n_(lo)). The precise phase velocities (or modal indices)of the fast and slow modes of the grating layer can be obtained byemploying analytic or numeric solution of the Helmholtz equation withperiodic boundary conditions imposed by the grating layer dimensions Λand f. This procedure and relevant means such as mode solver softwareare conventionally employed for designing or characterizing diffractiongratings, optical waveguides, or other optical components or structures.

The diffraction efficiency of the negative first transmitted diffractedorder is affected by the phase difference between fast and slow modesthat is accrued after propagation through the grating layer thickness d.If that phase difference is about equal to π (or another odd multiple ofπ) at a specified wavelength of interest, maximum diffraction efficiencyinto the first transmitted order is achieved for that grating layerconfiguration. The magnitude of the phase difference is related to theproduct of grating thickness d and refractive index difference. A largerindex contrast between n_(lo) and n_(hi) enables a smaller grating layerthickness d to be employed to achieve a given accrued phase difference.This is illustrated in FIG. 3, where the grating thickness required foroptimal diffraction efficiency (i.e., an accrued phase difference of π)is plotted as a function of index difference Δ=(n_(hi)−n_(lo)), which isvaried for this plot by varying n_(hi) while n_(lo) remains constant.The graph shows plots for n_(lo)=1.0, 1.5, and 2.0, roughlycorresponding to air, glass or silica, and silicon oxynitride fillingthe second grating regions 102 of grating layer 100. For the plots ofFIG. 3, a TE-polarized input signal with λ=1545 nm incident atθ_(in)=45.565° was used. FIG. 3 demonstrates that optimal diffractionefficiency can be achieved for relatively thin grating layers for indexcontrast>0.5. For example, a grating layer comprising silicon oxynitride(n_(hi)=2.0) etched to form grating regions 101 with grating regions 102left unfilled (n_(lo)=1.0) yields an optimal grating thickness of only1.7 μm. FIG. 3 indicates that the use of high index materials (n>1.5)and an index contrast>0.5 can yield high diffraction efficiency withthinner grating layers than can be achieved with lower-index materialssuch as glass.

As described above, to achieve high diffraction efficiency the opticalphase difference between fast and slow modes accrued in propagatingthrough the grating layer should be about equal to an odd multiple of π.For a given wavelength that phase difference depends on both the gratinglayer thickness and the difference between the respective modal indices.Those indices, (and thus possibly their difference) are often differentfor the two principal polarizations states (TE and TM). To obtainsubstantially polarization independent behavior, the modal indexdifference for both principal polarizations should be about equal.

For a given grating mode (propagating through the grating layer), themodal index depends on the bulk refractive indices of the first andsecond grating regions and the specific morphology of the grating layer.For a grating layer comprising regions having simple rectangularcross-sections, the morphological parameters that affect the modal indexis the grating's duty cycle (for a given grating spacing). The specificdependence of the modal indices on the grating duty cycle can beobtained by employing analytic or numeric solution of the Helmholtzequation with periodic boundary conditions imposed by the grating layerdimensions Λ and f. This procedure and relevant means such as modesolver software are conventionally employed for designing orcharacterizing diffraction gratings, optical waveguides, or otheroptical components or structures.

Two limiting cases illustrate the duty cycle's influence on the modalindices of fast and slow modes. For small duty cycles (f<0.1), the modalindices will be close to the refractive index of the second gratingregion because most of the grating will consist of second grating regionlow index material. Likewise, for high duty cycles (f>0.9), the modalindices for fast and slow modes will be close to the refractive index ofthe high index first grating regions. The difference between modalindices will typically be the largest close to a duty cycle of about 0.5and smaller for very small and very large duty cycles.

To obtain substantially polarization independent high gratingefficiency, a duty cycle should be found for which the modal indexdifference is substantially similar for both polarizations. Besidesaforementioned analytical tools, diffractive optics software or gratingsoftware, such as GSOLVER©, can be used to determine this optimal dutycycle. For example, for a grating layer consisting of chosen first andsecond grating region materials, the negative first order diffractionefficiency can be calculated, as a function of layer thickness and forboth polarizations, for a given angle of incidence, a given centerwavelength, and a minimum selected duty cycle (e.g., starting with thesmallest duty cycle that is consistent with the resolution of the chosenfabrication method, such as the minimum lithographic resolution, forexample). The grating layer thickness at which maximal diffractionefficiency occurs for each polarization is then recorded. The duty cycleis then incrementally increased and the calculation is repeated until aduty cycle is identified for which the peaks of maximal efficiency occurfor about the same grating layer thickness and are about the same heightfor both polarizations. A grating having that grating duty cycle andgrating layer thickness will exhibit nearly polarization independentbehavior.

Alternatively, a grating duty cycle can be selected for which themaximal efficiency for each polarization occurs at slightly differentthicknesses (for the given center wavelength and angle of incidence). Ifa grating is designed and fabricated with a duty cycle and a thicknesscorresponding to the point where the negative first order diffractionefficiency is the same for both polarizations at the given centerwavelength and angle of incidence (i.e., the crossing point in betweenthe peaks of the efficiency versus thickness plots of the twopolarizations), the resulting grating will typically exhibit diffractionefficiency at that wavelength that is substantially polarizationindependent, i.e., zero polarization dependent loss (PDL). Thatthickness is typically near the average of the thicknesses where maximalefficiency occurs for the two principal polarizations.

When using high refractive index layers and large index differentials tocreate a grating layer, it can be advantageous to impedance match thegrating layer to the adjacent media (i.e., surrounding superstrate andsubstrate). In FIG. 4A, a layer of titanium dioxide (n_(hi)=2.2) isetched to yield a grating with period Λ=1063.8 nm and a duty cycle of54%. FIG. 4D shows the calculated diffraction efficiency of theresulting grating layer 401 as a function of grating layer thicknesswhen no fill material is used in the second grating regions(n_(lo)=1.0). In each of FIGS. 4D-4F, the two main peaks correspond to aphase difference between two mode propagating through the grating layerabout equal to an odd multiple of π, while the troughs between thosepeaks correspond to a phase difference about equal to an even multipleof π. The diffraction efficiency curve of FIG. 4D exhibits significantoscillations superimposed on the two main peaks as the grating layerthickness varies. It is speculated that these arise from resonantbehavior of the internal grating modes reflected at the surfaces ofgrating layer 401. This oscillatory behavior requires tight toleranceson the etch depth to yield a grating maximally efficient at a particulardesign wavelength, which is problematic since the depth of a typicaletch process is controlled by timing and is often no more accurate thanabout 10% of the target depth.

The grating layer 401 can be impedance matched to the adjacent medium byan impedance matching layer on the corresponding surface of the gratinglayer 401. Such an impedance matching layer tends to suppress theoscillatory behavior shown in FIG. 4D. Impedance matching can beprovided by an anti-reflection layer between the grating layer and theadjacent medium. In FIG. 4B, a 340-nm thick impedance matching layer 402is provided on grating layer 401. The bulk refractive index of impedancematching layer 402 in this example is n=1.34 (close to that of MgF₂).FIG. 4E shows the calculated diffraction efficiency of the structure ofFIG. 4B as a function of grating layer thickness, in which theoscillations are substantially reduced. In FIG. 4C, a second impedancematching layer 403, having the same thickness and index as layer 402, isprovided on the other surface of grating layer 401. FIG. 4F shows thecalculated diffraction efficiency of the structure of FIG. 4C as afunction of grating layer thickness, in which the oscillations have beensubstantially eliminated. The structure of FIG. 4C exhibits >90%diffraction efficiency for both TE and TM input optical signals over awavelength range of at least 1525 to 1565 nm.

The impedance matching layers can be designed, i.e., suitable thicknessand bulk refractive index can be chosen, using the Fresnel equations toproduce a single-layer, quarter-wave antireflection coating. Thethickness of the layer is designed so that an optical phase differenceof π+2Nπ (i.e., an odd multiple of π where N is an integer) arisesbetween the reflection of an optical signal from the first and secondsurfaces of the layer at a selected wavelength and a selected angle ofincidence. Smaller values of N provide for impedance matching that iseffective over a wider spectral range. Larger values of N provide moreeffectively averaging over the spatially varying index of the gratinglayer (to a first approximation, an average of n_(lo) and n_(hi),weighted by the duty cycle). The refractive index of the impedancematching layer is chosen, for the selected wavelength and angle ofincidence, so that the magnitudes of the Fresnel reflection coefficientsfor reflection from the two surfaces of the impedance matching layer areequal or as closely equal as practicable given the available, compatiblematerials. Analytical or numerical calculations can be performed toapproximate or refine the optimum parameters of the impedance matchinglayer.

One example of fabricating an optical grating with two impedancematching layers is illustrated schematically in FIGS. 5A and 5B. First,an impedance matching layer 501 is deposited on a suitable substrate502. Then a transmission grating layer 503 is formed by depositing ahigh index layer on impedance matching layer 501 and then forming thegrating layer 503, e.g., by photolithography and etching. Third, asecond impedance matching layer 505 is formed on a second substrate 504,which is then pressed onto the grating layer 503 and held in place byoptical contacting. To further secure the layers, the edge of theoptical grating can be coated or sealed with epoxy or other suitableadhesive. Alternatively, an epoxy or other optical adhesive or opticalcement can be employed to fill the etched spaces in the high indexgrating material and also serve to hold the impedance matching layer 505and substrate 505 in place. If such a space-filling adhesive is used,the impedance matching layer 505 is optimized based on the average indexof the grating layer 503 with its second grating regions filled with theadhesive.

A specific exemplary embodiment is shown in FIG. 6 and is designed foran incidence angle of 50°. The transmission grating is formed on a fusedsilica substrate 600 (n=1.446). The grating layer comprises a 2-μm thicklayer 601 of CeO₂ (n=2.2) that is etched through and then filled withborophosphate glass 602 (n=1.446). Layer 602 functions both as animpedance matching layer and the dielectric material filling the secondgrating regions between the first regions 601. The thickness of layer602 beyond the top of layer 601 is 1.57 μm, and serves as the impedancematching layer. The grating period is 1.035 μm and the duty cycle 60%,i.e., the CeO₂ segment width is 621 nm and the glass-element width is414 nm. The grating structure rests on a 200 nm thick layer 603 of Al₂O₃(sapphire, n=1.7) that serves as a second impedance matching layer. Thegrating is optimized for operation as a demultiplexer in the ITU telecomC-band, 1525-1565 nm. The device shown in FIG. 6 can be fabricated usingvarious suitable methods known in the semiconductor industry includingbut not limited to the techniques of electron-beam vacuum deposition,photolithography, reactive-ion etch, and thermal anneal. Note that anyof the specific aforementioned materials can be replaced by others ofsimilar optical properties, i.e., refractive index, transparency, etc.

FIG. 7 shows the calculated diffraction efficiency of the −1 transmittedorder (t⁻¹ in the geometry of FIG. 1B) for TE-polarized (dashed line)and TM-polarized (solid line) input optical signals at an incidenceangle of 50°, which is approximately the Littrow condition for thecenter of the wavelength range shown in the plot. Both TE- andTM-polarized input optical signals are diffracted with significantlybetter than 90% diffraction efficiency over a wavelength range of1525-1565 nm. The polarization-dependent loss (PDL), i.e., theefficiency difference between the two polarizations, is well below 0.25dB across that range. Such operational performance is highly desirablefor devices employed in DWDM telecommunications systems, such as staticor reconfigurable optical add-drop multiplexers or optical switches.

Grating performance similar to that shown in FIG. 7, i.e., >90%diffraction efficiency for both TE and TM input and <0.25 dB PDL from1525 nm to 1565 nm, is still obtained even when operational ordimensional parameters deviate somewhat from the specific values givenabove. For example, FIGS. 8A and 8B show that the specified performanceis obtained for incidence angles of 45° and 55°, respectively. Detailedsimulation studies indicate that grating depth, duty cycle, and thethickness of layer 603 can deviate from the specific values of FIG. 6 byabout ±10% and the target performance of >90% diffraction efficiency forboth TE and TM input and <0.25 dB PDL is still obtained.

Another exemplary embodiment is shown in FIG. 9. It comprises a fusedsilica substrate 900 (n=1.446), a 2-μm-thick layer 901 of TiO₂ (n=2.2)that is etched and filled with borophosphate glass 902. The thickness oflayer 902 beyond the top of layer 901 is 1.5 μm. Layer 902 is coatedwith an anti-reflection coating 903 optimized to minimize reflection forlight incident at 45.565°. The grating period is 1.0638 μm and its dutycycle 60%, i.e., the TiO₂ segment width is 638 nm and the SiO₂-elementwidth is 425 nm. Layer 902 functions both as impedance matching layer aswell as to fill the spaces in grating layer 901. The grating layer 901rests on a 240 nm thick layer 904 of silicon oxynitride (n=1.77) thatacts as an impedance matching layer. The bottom of substrate 900 is alsoantireflection coated with coating 905. The grating is optimized foroperation as a demultiplexer in the ITU telecom C-band, 1525-1565 nm,and exhibits performance characteristics similar to those shown in FIGS.7, 8A, and 8B.

Generally, operationally acceptable grating performance can includeperformance in terms of diffraction efficiency andpolarization-dependent loss such as that shown in FIGS. 7, 8A, and 8B,but should not be viewed as limited to such values. Rather, differentoptical grating applications may have more or less stringentrequirements for grating performance and the term operationallyacceptable performance is defined in the context of the relevantapplication.

Another exemplary embodiment, optimized for an incidence angle of 50°,is shown in FIG. 10. Substrate 1000 comprises fused silica or a similarmaterial (n=1.446). A 2.2 μm (dimension b) thick layer 1002 ofsubstantially transparent dielectric material has refractive index n=2.2and is etched 2 μm deep (dimension e) and filled with a second material1003 with an index of 1.446 such as boron phosphorus-doped silica glass.The thickness c of layer 1003 beyond the top of layer 1002 is 0.9 μm(not shown to scale) and acts as an impedance matching layer. Layer 1003is coated with an anti-reflection coating 1004 optimized to minimizereflection for light incident at 50°. Since the reflection coefficientfor p-polarized input at the interface of layer 1003 to air is smallerthan that for s-polarized light (due to the incidence angle being closeto Brewster's angle) it may be advantageous to optimize theantireflection layer 1004 minimize the reflection of s-polarized light.The grating period is 1.035 μm and the duty is cycle 60%, i.e.,dimension d (defined for a grating ridge with non-vertical sidewalls asthe width of the ridge at half of its height) is 620 nm. The gratinglayer 1002 rests on a layer 1001 (a=230 nm thick) with refractive indexn=1.7. Layer 1001 can comprise sapphire deposited by conventionalmethods, but other optical materials of similar refractive index andproperties can also be employed to yield operationally acceptableperformance. The bottom of substrate 1000 can be antireflection coated(not shown). The grating is optimized for operation as a demultiplexerin the ITU telecom C-band, 1525-1565 and exhibits performancecharacteristics similar to those shown in FIGS. 7, 8A, and 8B. Otherapplication areas, for this and other disclosed embodiments, can includeoptical channel monitoring, multiplexing and non-telecom functions suchas spectroscopy.

Optimization of the grating layer thickness for both polarizationsstates is described above, as well as differing criteria that can beemployed for selecting an optimum combination of grating layer thicknessand duty cycle to achieve desired performance of the resulting grating.In a similar fashion, impedance matching layers can be optimized for oneor the other polarization states, or a compromise can be selected thatprovides desired grating performance over a range of wavelengths or fordiffering polarization states. In one example, an index and thicknessfor an impedance matching layer can be selected that minimizesreflection of one polarization state from the corresponding surface ofthe grating layer. Typically, the s-polarization state would be selectedfor such optimization, since that polarization state typically exhibitshigher reflectivity from an interface than the p-polarization state. Inanother example, the impedance matching layer index and thickness can beselected to minimize reflection of unpolarized light. In anotherexample, the thickness and index of the impedance matching layer can beselected that is not optimized for any particular polarization state,but that reduces or minimizes variation of grating performance betweendiffering polarization states.

In a further example of optimization of an optical grating, thicknessesof the grating layer and impedance matching layers, determined for eachlayer individually as described elsewhere herein, can be varied fromthose predetermined values to alter the overall performance of theresulting optical grating. For example, the grating layer thickness candiffer from that determined by maximizing its diffraction efficiency andthe impedance matching layer thicknesses can differ from those optimizedto minimize their reflectivities in a way that reduces or minimizesvariation of the grating performance with respect to wavelength orpolarization state. Those and many other “global” optimization or designschemes shall fall within the scope of the present disclosure orappended claims.

Some exemplary embodiments disclosed herein are shown having gratingstructures with vertical sidewalls. However, gratings structures havingnon-vertical sidewalls can also yield operationally acceptableperformance. For example, in the exemplary embodiment of FIG. 10, asidewall angle in the range α=84-90° yields optical grating performancewherein both s- and p-polarized input are diffracted into the firstorder with more than 90% efficiency and the polarization-dependent lossis less than 0.25 dB (for angles of incidence 50°±5°).

Additional exemplary embodiments are shown in FIGS. 11A and 11B. Alldimensions, materials, refractive indices and other optical propertiesare the same as those of FIG. 10, except for the thickness dimension band etch depth e. For both FIGS. 11A and 11B, b=2 μm. In FIG. 11A, theetch depth e>2.23 μm, i.e., both the grating layer and the lowerimpedance matching layer are etched through. In FIG. 11B, the etch depthe=2.0 μm, i.e., only the grating layer is etched. Per simulation, theembodiments of FIGS. 11A and 11B yield greater than 90% efficiency forboth s- and p-polarized input and the polarization-dependent loss willbelow than 0.25 dB (for angles of incidence 50±5°) for sidewall angle inthe range α=81-90° (FIG. 11A) and α=84-90° (FIG. 11B), respectively.

Another exemplary embodiment, optimized for an incidence angle of 50°,is shown in FIG. 12. The substrate 1200 comprises fused silica orsimilar material (n=1.446). A 1.1 μm (dimension c) thick layer 1201 withrefractive index n=2.2 is etched 1 μm deep (dimension e). The trenchesof the grating layer 1201 remain unfilled. The tops of the gratingridges or “teeth” are covered with impedance matching layer 1202 ofthickness b=300 nm and refractive index 1.444. Unlike impedance matchinglayers of previous exemplary embodiments, which are substantiallycontinuous, impedance matching layer 1202 comprises multiple, discrete,elongated regions that are positioned on a corresponding first gratingregion of grating layer 1201 (i.e., the grating ridges). Layer 1202functions both as antireflection-coating and impedance matching layerfor the grating layer 1201. The grating period is 1.035 μm and the dutycycle is 56%, i.e., dimension d is 580 nm. The grating layer 1201 restson an impedance matching layer 1203 of thickness a=230 nm of materialwith refractive index n=1.7. For example, layer 1203 can comprisesapphire or glassy/amorphous Al₂O₃ and can be formed using any suitabletechniques. Other optical materials of similar refractive index andproperties can also be employed to yield operationally acceptableperformance. The bottom of substrate 1200 can also be antireflectioncoated (not shown). As with previous embodiments, other specificmaterial with corresponding refractive indices and thicknesses can beemployed to provide essentially equivalent performance. Simulationsdescribed above can be employed for determining tolerances the variousgrating design parameters. The grating of FIG. 12 is optimized foroperation as a demultiplexer in the ITU telecom C-band, 1525-1565 nm,and exhibits performance characteristics similar to those shown in FIGS.7, 8A, and 8B. The design incidence angle is 50°, but similarperformance is exhibited for angles of incidence of 50°±5°.

The exemplary optical grating of FIG. 12 can be formed depositing layers1201 and 1202 on top of layer 1203 on the substrate 1200, then etchingthrough layer 1202, and then etching layer 1201 to e=1 μm.Alternatively, layer 1201 can be deposited and then etched, and thenlayer 1202 can be deposited using a non-conformal deposition (i.e.,top-down directional deposition). Such a process forms coating 1202 inthe bottoms of the trenches between the grating ridges (not shown). Thiscan be advantageous by providing additional impedance matching to thehigh index layer 1201 at the trench bottom. The grating structure ofFIG. 12 provides operationally acceptable performance for non-verticalside walls throughout the approximate range of α=78-90°.

Variations of the embodiment of FIG. 12 are shown in FIGS. 13A and 13B.All dimensions, materials, refractive indices and other opticalproperties in FIGS. 13A and 13B are the same as those of FIG. 12 exceptfor the thickness dimension c and etch depth e. For both FIGS. 13A and13B, c=1 μm. In the embodiment of FIG. 13B, the etch depth e>1.23 μm,i.e., layers 1301, 1302 and 1303 are all etched through. Alternatively,layers 1301 and 1303 are etched through and layer 1302 is depositedafterward in a top-down (i.e., non-conformal) manner. The indices ofsubstrate 1300 and layer 1302 are preferably substantially equal to oneanother in that arrangement. In the embodiment of FIG. 13A, the etchdepth e=1.0 μm, i.e., only layers 1301 and 1302 are etched. Theembodiments of FIGS. 13A and 13B provide operationally acceptableperformance for non-vertical sidewall angles throughout the approximaterange of α=78-90°.

Another exemplary embodiment, designed for an incidence angle of 46.56°,is shown in FIG. 14. The optical transmission grating is formed on afused silica substrate 1400 (n=1.446), and comprises a 1.025-μm thicklayer 1401 of SiN (n=2.2) that is sandwiched between a lower impedancematching layer 1402 comprising silicon oxynitride (Si_(x)ON_(y), n=1.7)and an upper impedance matching layer 1403 comprising silicon dioxide(n=1.45). All materials can be deposited by plasma-enhanced chemicalvapor deposition or physical vapor deposition or other conventionalthin-film deposition processes. The grating period is 1.0638 μm and theduty cycle 56%, i.e., the grating line width is 596 nm and the trenchwidth is 468 nm. The grating is optimized for operation as ademultiplexer in the ITU telecom C-band, 1526-1566 nm. FIG. 14explicitly lists tolerances for materials refractive indices, layerthicknesses, sidewall angle, duty cycle, and etch depth that yieldoperationally acceptable device performance. Useful gratings can beformed with parameters outside the tolerance range indicated. Thegrating will also function acceptably if the trench is etched too deep,i.e., the etch extends into the fused silica substrate, or too shallow,i.e., a residual layer of silicon oxynitride is left on the substrate.The tolerances given in FIG. 14 are exemplary and should not be viewedat constraining the scope of the present disclosure or appended claims.Depending on the specific application, acceptable performance may bereached without meeting these specific tolerances.

FIG. 15 shows simulated grating performance over the wavelength rangefor the optical grating of FIG. 14. FIG. 16 shows the simulatedperformance in graphical and tabular form when the input angle is varied±2° about the design angle. FIG. 17 contains a table specifying gratingperformance, specifically minimum diffraction efficiency (DE) andmaximum polarization-dependent loss (PDL) over a wavelength range of1526-1566 nm, when grating dimensions, refractive indices and otherparameters are varied. The first column specifies the parameter beingvaried, and the second column the amount of variation. The third andfourth columns show the resulting performance parameters (DE and PDL)and the fifth and sixth columns show the change of those parameters fromthose obtained under the optimized conditions as shown in FIG. 15.

Another exemplary embodiment, designed for an incidence angle of 46.56°,is shown in FIG. 18. The optical transmission grating is formed on afused silica substrate 1800 and comprises a 1.13-μm thick layer 1801 ofSiN (n=2.05) that is sandwiched between a lower impedance matching layer1802 comprising silicon oxynitride (Si_(x)ON_(y), n=1.7), and an upperimpedance matching layer 1803 comprising silicon dioxide (n=1.46). Allmaterials can be deposited by plasma-enhanced chemical vapor depositionor other conventional thin-film deposition. The grating period is 1.0638μm and the duty cycle 57%, i.e., the grating line width is 606 nm andthe trench width is 457 nm. The grating is optimized for operation as ademultiplexer in the ITU telecom C-band, 1526-1566 nm. FIG. 18explicitly lists tolerances for material refractive indices, layerthicknesses, sidewall angle, duty cycle, and etch depth that yieldoperationally acceptable grating performance. The grating will alsofunction acceptably if the trench is etched too deep, i.e., if thetrench extends into the fused silica substrate, or too shallow, i.e., aresidual layer of silicon oxynitride is left on the substrate. Thetolerances given in FIG. 18 are exemplary and should not be viewed at aconstraining the scope of the present disclosure or appended claims.Depending on the specific application, acceptable performance may bereached without meeting these specific tolerances.

FIG. 19 shows the simulated grating performance over the wavelengthrange for the grating of FIG. 18. FIG. 20 contains a table specifyinggrating performance, specifically minimum diffraction efficiency andmaximum polarization-dependent loss, when grating dimensions, refractiveindices, and other parameters are varied from the optimized design ofFIG. 18, in a form similar to that of FIG. 17. The changes in DE and PDLin the table of FIG. 20 are with relative to the performance shown inFIG. 19.

Another exemplary embodiment, designed for an incidence angle of 50°, isshown in FIG. 21. The optical transmission grating is formed on a fusedsilica substrate 2100 and comprises a 0.44-μm thick layer 2101 ofamorphous silicon (n=3.48) that is sandwiched between a lower impedancematching layer 2102 comprising silicon nitride (SiN, n=2.18) and anupper impedance matching layer 2103 comprising silicon oxynitride(Si_(x)ON_(y), n=1.67). All materials can be deposited byplasma-enhanced chemical vapor deposition or other conventionalthin-film deposition. The grating period is 1.035 μm, the grating linewidth is 393 nm, and the grating trench width is 642 nm. The grating isoptimized for operation as a demultiplexer in the ITU telecom C-band,1526-1566 nm. Other similar materials maybe substituted for those shownin FIG. 21. For example, the top impedance matching layer 2103 couldcomprise aluminum oxide and the bottom impedance matching layer couldcomprise titanium dioxide or tantalum pentoxide.

Referring back to FIG. 1C, grating layer 100 is arranged as a reflectiongrating. Many of the features and parameters applicable to thetransmission gratings described above are also applicable to reflectiongratings described below. The adjacent medium above the reflectiongrating is air or another inert gas. The grating layer 100 is positionedon a reflective layer or set of layers 103 that is highly reflectiveover the operational wavelength and angular range of interest. Thereflective layer 103 can be a metal layer or thin-film multilayerdielectric stack arranged to provide high reflectivity. The gratinglayer 100 and reflective layer 103 rest on a substrate 104 thatcomprises any suitable material, including but not limited to silicon,fused silica, quartz, borosilicate glass, borophosphate glass, or sodalime glass.

In FIG. 1C, an incident optical signal with wavevector k_(in) isincident on the grating layer 100. In this example the signal's incidentangle θ_(in) (with respect to the grating normal) is chosen so that themagnitude of the incident signal's wavevector component along the x-axisis about equal to half of the grating wavevector magnitude. Thatgeometry results in a reflected diffracted wave with wavevector k_(r-1)that is approximately collinear but anti-parallel with the input signal(reflected negative first order diffracted signal). Wavevector k_(r0)denotes the specularly reflected signal (zeroth order diffractedsignals).

The diffraction efficiency of the reflected negative first orderdiffracted signal depends on the thickness d of the grating as well asthe bulk refractive indices n_(hi) and n_(lo) of the first and secondgrating regions 101 and 102, respectively, in a manner similar to thetransmission gratings described above. For appropriately chosen gratingthickness and refractive indices, greater than 90% of the incidentoptical signal can be diffracted into the first reflected diffractedorder. Additionally, the duty cycle of the grating can be optimizedalong with the bulk indices and thickness to reduce thepolarization-dependence of the diffraction efficiency into the firstdiffracted order, as described further below.

As described above, the incident optical signal couples into the “fast”and “slow” bound modes that propagate perpendicular to the grating layer100 (as in FIGS. 2A and 2B). The diffraction efficiency of the negativefirst reflected diffracted order is affected by the phase differencebetween fast and slow modes that is accrued after propagation twicethrough the grating layer thickness d, with reflection by layer 103. Ifthat phase difference is about equal to π (or another odd multiple of π)at a specified wavelength of interest, maximum diffraction efficiencyinto the first reflected order is achieved for that grating layerconfiguration. The magnitude of the phase difference is related to theproduct of grating thickness d and refractive index difference. A largerindex contrast between n_(lo) and n_(hi) enables a smaller grating layerthickness d to be employed to achieve a given accrued phase difference,just as with the transmission gratings described previously.

The reflection grating of FIG. 1C will exhibit oscillatory behavior ofits diffraction efficiency with respect to grating layer thicknessentirely analogous to the behavior illustrated in FIGS. 4A-4F fortransmission gratings. That oscillatory behavior can mitigated by animpedance matching layer between the grating layer and an adjacentmedium. In the case of a reflection grating, however, only one impedancematching layer is required; the reflective layer occupies the secondsurface of the grating layer.

FIG. 22 shows an exemplary embodiment of a reflection grating with animpedance matching layer. The reflection grating layer 2301 is formed ona fused silica substrate 2300 (n=1.446) and comprises a 600-nm thicklayer of silicon nitride (n=2.05) that is etched and left unfilled(n_(lo)=1). The grating period is 1.0638 μm and the duty cycle 65%,i.e., the SiN ridge width is 691 nm and the width of the trench is 373nm. A SiO₂ layer 2302 on top of the silicon nitride grating functions asthe impedance matching layer. The grating structure rests on a 5-layerthin-film stack 2304 consisting of alternating layers of amorphoussilicon (n=3.71, 102 nm thick) and SiO₂ (n=1.46, 300 nm thick) thatfunctions as the reflective layer. The grating is optimized foroperation in the ITU telecom C-band, 1525-1565 nm, at an angle ofincidence of 45°. The optical grating of FIG. 22 can be fabricated usingany suitable conventional methods, including those used in thesemiconductor industry. Examples include but are not limited toelectron-beam vacuum deposition, photolithography, reactive-ion etching,and thermal annealing. Any of the specific materials can be replaced byothers of similar optical properties such as transparency, refractiveindex, and so forth.

The impedance matching layer 2302 can be designed as described above fortransmission grating impedance matching layers, i.e., the thickness andsuitable refractive index can be calculated using the Fresnel equations.The thickness of the layer 2302 is designed so that an optical phasedifference of about π+2Nπ (an odd multiple of π for an integer N),arises between the reflection from the first surface (top, air-SiO2interface in FIG. 22) and the second surface (bottom, SiO₂—SiNinterface) of the layer 2302. Smaller values of N provide for impedancematching that is effective over a wider spectral range. Larger values ofN provide more effectively averaging over the spatially varying index ofthe grating layer 2301 (to a first approximation, an average of n_(lo)and n_(hi), weighted by the duty cycle). The refractive index of theimpedance matching layer is chosen, for the selected wavelength andangle of incidence, so that the magnitudes of the Fresnel reflectioncoefficients for reflection from the two surfaces of the impedancematching layer are equal or as closely equal as practicable given theavailable, compatible materials. Analytical or numerical calculationscan be performed to approximate or refine the optimum parameters of theimpedance matching layer.

In some instances, the phase change upon reflection from the reflectinglayer may differ for the fast and slow modes. In such a case, to achievehigh diffraction efficiency, an accrued optical phase difference betweenslow and fast modes equal to about an odd multiple of π is needed thatincludes portions accrued during propagation through the grating layeras well as the phase difference that arises upon reflection.

As described above, the difference between modal indices n_(hi) andn_(lo) is often different for the two principal input polarizations TEand TM. Substantially polarization independent behavior of the highdiffraction efficiency can be obtained when the modal phase differenceis about equal to an odd multiple of π for both polarizations. That canbe achieved, at least approximately, by suitably tailoring the gratingmorphology, (i.e., grating duty cycle, grating layer thickness, and bulkrefractive indices of the two grating regions). In some instances, thephase shift upon reflection from the reflecting layer might differbetween the slow and fast modes and might also be polarizationdependent. If substantially polarization-independent grating behavior isdesired, the grating layer thickness, duty cycle, and indices must beselected so that the aggregate accrued phase difference (arising fromboth propagation through the grating layer and reflection) is aboutequal to an odd multiple of π for both polarizations. Achieving thatphase difference for both polarizations simultaneously may not bepossible for every combination of material indices, but a grating layerarrangement can typically be found that yields operationally acceptableperformance over a selected range of wavelengths. In some instanceswherein the aggregate phase difference between the two grating modesdepends upon these two independent structures (grating layer andreflector), a wider wavelength range over which operationally acceptableperformance (e.g., high efficiency or polarization independence) cansometimes be achieved by using one phase shift to at least partlycompensate for the other to achieve a phase difference about equal to anodd multiple of π over a larger spectral range than would be possiblewith the grating layer alone.

As is well know in the art of thin film optical coatings, reflectivedielectric stacks can be designed to have highly tailored reflectiveamplitude and phase properties. Those can be exploited to incorporateadditional functionality into the optical gratings disclosed herein. Forexample, the reflective layer can comprise a dielectric thin film stackwith one or multiple cavities that provide a non-linear overallreflective phase transfer function (as a function of incidentwavelength). Such a phase transfer function can be employed, e.g., tosteer the diffracted beam to output angles other than those dictated bythe grating equation and grating spacing. In another example, thereflective amplitude transfer function of the thin film reflector can beemployed to tailor the overall spectral response of the grating todesired behavior.

In some instances it may be advantageous to minimize the Fresnelreflection coefficient difference for both input signal polarizations,while in other instances it may not be possible or necessary. Forexample, the optical grating can be designed so that the angle ofincidence is close to Brewster's angle for the average refractive indexof the grating layer 2301, which minimizes the reflection coefficientfor p-polarized input light (or TM polarization). Optimization of theimpedance matching layer 2302 can be performed considering onlys-polarized input light (i.e., TE polarization) to minimize reflectionfrom the grating layer 2301. Simulated optical performance of theoptical reflection grating of FIG. 22 is shown in FIG. 23.

Another exemplary embodiment of an optical reflection grating is shownin FIG. 24. The grating layer 2501 is formed on top of a 100 nm-thickgold layer 2504 rather than the multi-layer stack of FIG. 22. Thegrating layer 2502 and gold layer 2504 rest on a silicon substrate 2500.All other parameters of the grating layer 2501 and the impedancematching layer 2502 are the same as for the grating of FIG. 22. Toenable adequate adhesion of the gold layer 2504 (and hence the gratinglayer 2501) to the silicon substrate 2500, use of an adhesion promotionlayer such as chromium might be desirable. Other metals, e.g., aluminumor silver, can be employed as the reflective layer 2504; certain othermetals, e.g., aluminum, have better adhesion properties than gold toboth the silicon substrate and the silicon nitride grating layer. Theoptical performance of the optical reflection grating of FIG. 24 isshown in FIGS. 25A and 25B. FIG. 25A shows the diffraction efficiency asa function of input wavelength for a fixed input angle of 45°. FIG. 25Bshows the diffraction efficiency as a function of input angle, with theinput wavelength varied to satisfy the Littrow condition (λ=2×Λ×sinθ_(in)) as the input angle is varied.

Reflection gratings made according to the teachings of the presentdisclosure also can be made highly efficient for diffractingarrangements other than that of Littrow incidence. FIGS. 26A-26C showthe diffraction efficiency as a function of grating layer thickness forthe reflection grating of FIG. 24 for differing diffraction geometries.The wavelength of the TE-polarized incident signal is 1.545 μm. Incidentand diffracted angle for the negative first diffracted order vary amongthe three graphs. For each incident angle, a grating layer thickness canbe identified for which the first order diffraction efficiency is morethan 90%. The grating has no diffracted orders for input angles <26.7°,and the diffracted beam is always located on the same side of thegrating normal as the input beam (since λ/Λ>1). Similarly, fortransmission gratings, strict adherence to a Littrow diffractivegeometry is not necessary, and high diffraction efficiency (>90%) andlow polarization-dependent loss may be achieved using the teachings ofthe present disclosure for other incidence angles andwavelength-to-grating-period ratios.

The graphs of FIGS. 27A-27C further demonstrate that the opticalgratings disclosed herein can be made highly efficient in non-Littrowdiffractive geometries. In FIGS. 27A and 27B, diffraction efficiency forthe device of FIG. 24 is plotted as a function of the thickness ofgrating layer 2501 for TE and TM polarized incident light, respectively.The wavelength of the incident signal is 1.545 μm. The incident angle is65° (rather than 45° as in FIG. 25A) and the output angle for thenegative first diffraction order is near −30°. The diffractionefficiency for both polarizations peaks near a grating layer thicknessof about 600 nm. FIG. 27C shows the diffraction efficiency plottedagainst input wavelength for the same input angle and unpolarized light.All other conditions and parameters are the same as those described forthe grating of FIG. 24. The grating is better than 80% efficient over alarge wavelength range (ca. 1.45-1.85 μm) for this non-Littrow incidencecondition. The diffraction efficiency can be improved by re-optimizingthe impedance matching layer 2502 (i.e., its refractive index, material,or thickness) from the parameters of FIG. 24 to those suitable for thenew incidence angle.

Another exemplary embodiment is shown in FIG. 28. The reflection gratingof FIG. 28 is similar to that of FIG. 24 in most dimensions, materials,and refractive indices, except that the grating trenches, which consistof air in FIG. 24 (n_(lo)=1), have been filled in with the samedielectric material (i.e., silicon dioxide) that provides impedancematching layer 2903 for the silicon nitride grating layer 2901. Becausethe index contrast between materials in the high index grating material2901 (silicon nitride) and the low index grating material 2902 (silicondioxide) is about half the contrast of the grating of FIG. 24, thegrating layer thickness is increased by a proportional factor to enableoptimized or operationally acceptable diffraction efficiency. Othermaterials including polymers or other materials that readily conform toirregular surface structure while still providing a flat outer surface,can be employed to fill the grating trenches.

Rather than forming the grating layer on top of the reflective goldlayer, as in FIGS. 24 and 28, it can be advantageous to form thereflective metal layer 3004 on top of the grating layer 3001/3002, asshown in exemplary embodiment of FIG. 29. In such an arrangement, theincident light must propagate to and from the grating layer through thesubstrate 3000 (fused silica in this example). The optical grating ofFIG. 29 can be fabricated by forming the grating layer 3001/3002 on thefused silica substrate 3000 and then depositing the reflective goldlayer on top of the grating layer. In an alternative procedure, shown inFIG. 30, a dielectric grating layer formed on a fused silica substrateis butted up against a second substrate that is coated with gold oranother reflective layer. The reflective layer can be held in place byoptical contacting, by mechanically clamping the two substratestogether, by bonding them with an appropriate optical adhesive orcement, or by another suitable methods. In the examples of FIGS. 29 and30, the grating layer comprises regions of SiN (higher index) andsilicon dioxide (lower index). In another exemplary embodiment (notshown) that can be particularly convenient to fabricate, a lower-indexpolymer can fill trenches between higher index grating ridges so as toform a substantially planar surface on which to deposit or contact thereflective layer. That flat surface can comprise a layer of polymer overthe grating layer, or can comprise the tops of the ridges of the gratinglayer and the intervening polymer-filled trenches. In the case that aseparate reflective layer is contacted with the grating layer, thepolymer can also act as an adhesive.

As described above, impedance matching layers are formed from a singlelayer of dielectric material having a refractive index and thicknessselected to suppress reflections at the surface of the grating layer.That arrangement is depicted schematically in FIG. 31A, with gratinglayer 3201 and impedance matching layers 3202 and 3203 formed onsubstrate 3000. Alternatively, one or both of the impedance matchinglayers in a transmission or reflection grating can be replaced by animpedance matching layer 3202 comprising a set of two layers (as in FIG.31B) or a set of multiple layers (as in FIG. 31C) that are arranged tosuppress reflections from the surface of the grating layer 3201. Suchbi- or multi-layer impedance matching structures can be designedaccording to conventional methods, such as those described in suchreferences as “Thin Film Optical Filters” by Angus McLeod (3ed,Institute or Physics, London, 2001), which is hereby incorporated byreference as if fully set forth herein. The spectral response of a bi-or multi-layer impedance matching structure can be designed, by themethods discussed in the reference, to transmit only selected spectralportions of light incident on the optical grating while reflecting orotherwise blocking other spectral portions. The ability to thus tailorthe spectral response of the impedance matching layer, in addition tothat of the grating layer, provides an additional means to influence theoverall spectral response of the optical grating. Alternatively, theimpedance matching layer can comprise sub-wavelength-scale structures,e.g., a periodic or aperiodic array of structural features that aresubstantially smaller than the wavelength of the incident light (as inFIG. 31D). Dimensions and refractive indices of the structural featurescan be selected so that the incident optical signal interacts with theimpedance matching layer as if it were a homogeneous medium having arefractive index and layer thickness optimized to reduce reflections atthe surface of the grating layer 3201. Such an arrangement enables theimpedance matching layer to be locally optimized in an optical gratinghaving, for example, a grating period or duty cycle that varies withposition, without resorting to layers of varying thickness, which areproblematic to fabricate. One example of such a sub-wavelength scalestructure is a so-called moth-eye structure comprisingsub-wavelength-sized pyramids of dielectric material. In the example ofFIG. 31D, the shaded and unshaded regions of thesub-wavelength-structured impedance matching layer 3202 comprisedielectric materials with differing refractive indices, with therelative volumes occupied by each material determining the effectiveindex of the layer. Alternatively, one of the regions can be leftunfilled, e.g., one of the constituent materials of the layer 3202 wouldbe air.

As described above, high diffraction efficiency was obtained byintroducing appropriate phase shifts between two propagating gratingoptical modes that propagate through the grating layer, and by limitingthe number of available diffracted orders by choosing suitable gratingperiod and incidence conditions. Operationally acceptable levels ofdiffraction efficiency can also be achieved in some cases whereinmultiple, i.e., more than two, grating modes or multiple diffractedorders are present. The presence of more than two grating modes can insome instances enable additional design flexibility for highly efficientgrating devices.

An exemplary embodiment of a transmission grating is shown in FIG. 32Aand comprises a fused silica substrate, an amorphous silicon gratinglayer (refractive index 3.48), a top impedance matching layer consistingof 190 nm silicon oxynitride (refractive index 1.67), and a bottomimpedance matching layer consisting of 260 nm titanium dioxide(refractive index 2.18). The grating period is 1.035 μm and the dutycycle 50%, i.e., the silicon ridge width is 517.5 nm and the width ofthe trench is 517.5 nm. The grating is optimized for operation in theITU telecom C-band, 1525-1565 nm, with an angle of incidence of 50°. Ananalysis of the grating modes propagating through the grating asdescribed above reveals the presence of three waveguide modes witheffective indices of about 1.2 (mode 1), 2.7 (mode 2), and 3.3 (mode 3).

FIG. 32B is a plot of the diffraction efficiency as a function ofgrating layer thickness into the first transmitted diffraction order forthe embodiment of FIG. 32A with an input wavelength of 1.545 μm, adesign incidence angle of 50°, and TE-polarized input. The diffractionefficiency peaks at grating layer thicknesses of 300 nm, 600 nm, 900 nm,1200 nm and 1500 nm. These are the thicknesses that correspond to aphase shift of π for, respectively, modes 1 and 3, modes 1 and 2, modes1 and 3, modes 2 and 3, and modes 1 and 2. At those thicknesses, the πphase shift results in substantial reduction of the zeroth transmittedorder and concomitant enhancement of the negative first transmittedorder. It is clear from FIG. 32B that high diffraction efficiency can beachieved in the presence of more than two propagating grating modes.

Optical transmission and reflection gratings as disclosed or claimedherein can be arranged to provide imaging, focusing, collimation, orother spatial manipulations of the diffracted optical signal, bysuitable variation of grating spacing on the grating or by suitablecurvature of the grating lines. Such arrangements of the grating linescan be designed by computed interference of simulated optical signals,as disclosed in U.S. Pat. No. 7,349,599 and U.S. Pat. Pub. 2007/0053635,each of which is hereby incorporated by reference as if fully set forthherein. To account for varying angular incidence conditions innon-collimated input it may be useful to locally optimize the gratingduty cycle to obtain an operationally acceptable level of diffractionefficiency or polarization dependent loss. FIG. 33A illustratesschematically computation of an interference pattern used to form atransmission grating. FIG. 33B illustrates schematically computation ofan interference pattern used to form a reflection grating. FIG. 34 is aschematic plan view of a grating layer arranged according to aninterference pattern calculated between a diverging input signal and aconverging output signal, wherein the grating lines vary in spacing andcurvature across the grating. That arrangement of the lines of thediffraction grating enables a flat optical grating, for example, toproduce a diffracted signal that differs from the input signal withrespect its convergence, divergence, or collimation properties. Such aflat, imaging grating can be used advantageously, for example, toreimage only one of several DWDM channels emerging from a first opticalfiber onto the entrance face of a second optical fiber without the needfor separate focusing elements.

Various materials have been disclosed for forming the exemplaryembodiments disclosed above. Any suitable material or combination ofmaterials can be employed for forming a grating layer, impedancematching layer, reflective layer, or substrate that exhibits suitabletransparency over the relevant operational wavelength range and suitablebulk refractive index. Suitable material can include, are not limitedto, silicon, doped silicon, silicon nitride, silicon oxynitride,titanium dioxide, cerium dioxide, aluminum oxide, tantalum pentoxide,aluminum oxynitride, beryllium oxide, bismuth oxide, chromium oxide,germanium, doped germanium, hafnium oxide, magnesium oxide, neodymiumoxide, praseodymium oxide, scandium oxide, zinc selenide, zinc sulfide,zirconium oxide, silica, doped silica, borophosphate glass, borosilicateglass, soda lime glass, polymer, beryllium oxide, calcium fluoride,cerium fluoride, cryolite, hafnium fluoride, lanthanum fluoride,strontium fluoride, ytterbium fluoride, ambient atmosphere, air, orinert gas.

It is intended that equivalents of the disclosed exemplary embodimentsand methods shall fall within the scope of the present disclosure orappended claims. It is intended that the disclosed exemplary embodimentsand methods, and equivalents thereof, may be modified while remainingwithin the scope of the present disclosure or appended claims.

For purposes of the present disclosure and appended claims, theconjunction “or” is to be construed inclusively (e.g., “a dog or a cat”would be interpreted as “a dog, or a cat, or both”; e.g., “a dog, a cat,or a mouse” would be interpreted as “a dog, or a cat, or a mouse, or anytwo, or all three”), unless: (i) it is explicitly stated otherwise,e.g., by use of “either . . . or”, “only one of . . . ”, or similarlanguage; or (ii) two or more of the listed alternatives are mutuallyexclusive within the particular context, in which case “or” wouldencompass only those combinations involving non-mutually-exclusivealternatives. For purposes of the present disclosure or appended claims,the words “comprising,” “including,” “having,” and variants thereofshall be construed as open ended terminology, with the same meaning asif the phrase “at least” were appended after each instance thereof.

What is claimed is:
 1. An optical transmission grating positioned withinan ambient medium, the ambient medium being substantially transparentover an operational wavelength range and characterized by an ambientmedium refractive index n_(A), the optical transmission gratingcomprising: (a) a substrate comprising a non-gaseous material that ischaracterized by a substrate refractive index n_(S) and substantiallytransparent over an operational wavelength range; (b) a first impedancematching layer of thickness t₁ on a first surface of the substrate, thefirst impedance matching layer comprising a first non-gaseous dielectricmaterial that is characterized by a refractive index n₁ andsubstantially transparent over the operational wavelength range; (c) aset of multiple, discrete, spaced-apart, elongated ridges of thicknesst₂ protruding from the first impedance matching layer away from thesubstrate and separated by intervening grooves, the ridges comprising asecond dielectric material that is characterized by a refractive indexn₂ and substantially transparent over the operational wavelength range;and (d) a second impedance matching layer covering the ridges to athickness t₃ above each ridge and substantially filling the grooves, thesecond impedance matching layer comprising a third dielectric materialthat is characterized by a refractive index n₃ and substantiallytransparent over the operational wavelength range, wherein: (e) for atleast a first localized area of the grating, the set of ridges ischaracterized by a first grating spacing Λ, a first ridge width w<Λ, anda first grating wavevector direction; (f) a bottom surface of the seconddielectric material of each ridge is in contact with the firstdielectric material of the first impedance matching layer, and top andside surfaces of the second dielectric material of each ridge are incontact with the third dielectric material of the second impedancematching layer; (g) over at least the operational wavelength range, (i)n₁ differs from n_(S) and n₂, and (ii) n₃ differs from n₂ and n_(A); (h)for at least one selected incidence angle θ_(in) and at least oneselected wavelength λ within the operational wavelength range, the setof ridges is structurally arranged in the first localized area of thegrating so that the first grating spacing Λ results in an optical signalincident from the ambient medium at θ_(in) on the first localized areabeing at least partly diffracted into one or more transmitted diffractedorders in the substrate bulk at corresponding diffracted angles θ_(d,m)that satisfy n_(A) sin θ_(in)+n_(S) sin θ_(d,m)=mλ/Λ where m is aninteger; and (i) the set of ridges and the first and second impedancematching layers are structurally arranged in the first localized area ofthe grating so that n_(A), n_(S), n₁, n₂, n₃, t₁, t₂, t₃, and w resultin a diffraction efficiency greater than 90% into the transmitteddiffracted orders for which m=±1.
 2. The optical transmission grating ofclaim 1 wherein, for the selected incidence angle θ_(in) and theselected wavelength λ, the set of ridges and the first and secondimpedance matching layers are structurally arranged in the firstlocalized area of the grating so that the first grating spacing Λresults in an optical signal incident from the ambient medium at θ_(in)on the first localized area being at least partly diffracted into only asingle transmitted diffracted order in the substrate bulk for which m=±1and into only a single reflected diffracted order in the ambient mediumfor which m=±1.
 3. The optical transmission grating of claim 1 whereinn₂>n₁>n_(S) and n₂>n₃>n_(A) over at least the operational wavelengthrange.
 4. The optical transmission grating of claim 1 wherein the set ofridges and the first and second impedance matching layers arestructurally arranged in the first localized area of the grating so thatn_(A), n_(S), n₁, n₂, n₃, t₁, t₂, t₃, and w result in variation withpolarization of the transmitted diffraction efficiency that is within±0.25 dB of the transmitted diffraction efficiency.
 5. The opticaltransmission grating of claim 1 wherein the set of ridges is arrangedaccording to an interference pattern derived from computed interferenceat the substrate surface between a simulated design input optical signaland a simulated design output optical signal, which simulated signalsdiffer from one another with respect to convergence, divergence, orcollimation properties.
 6. The optical transmission grating of claim 1wherein the substrate is substantially flat, and the set of ridges isarranged so that respective wavefronts of an incident optical signal anda portion of that signal diffracted into the transmitted diffractionorder exhibit differing convergence, divergence, or collimationproperties.
 7. The optical transmission grating of claim 1 wherein thefirst dielectric material separates the substrate material from thethird dielectric material at the bottom of each groove.
 8. The opticaltransmission grating of claim 1 wherein the grooves extend at leastpartly through the first impedance matching layer.
 9. The opticaltransmission grating of claim 8 wherein the third dielectric materialand the substrate material are in contact at the bottom of each groove,thereby separating the first impedance matching layer into multiple,discrete, elongated regions of the first dielectric material.
 10. Theoptical transmission grating of claim 1 wherein the second dielectricmaterial separates the first and third dielectric materials at thebottom of each groove.
 11. The optical grating of claim 1 wherein: n_(S)is between about 1.4 and about 1.5; n₁ is about 1.7; n₂ is greater thanabout 2; and n₃ is between about 1.4 and about 1.5.
 12. The opticalgrating of claim 11 wherein: the substrate comprises silica or dopedsilica; the first dielectric material comprises aluminum oxide orsilicon oxynitride; the second dielectric material comprises ceriumoxide or titanium oxide; and the third dielectric material comprisessilica or doped silica.
 13. The optical grating of claim 11 wherein, forat least the first localized area of the grating layer: Λ is about 1 μm;w is about 0.6 μm; t₂ is about 2 μm; t₁ is between about 0.2 μm andabout 0.3 μm; and t₃ is between about 0.9 μm and about 1.6 μm.
 14. Theoptical transmission grating of claim 13 wherein the operationalwavelength range is between about 1525 nm and about 1565 nm.
 15. Theoptical transmission grating of claim 1 further comprising anantireflection coating on the second impedance matching layer betweenthe ambient medium and the third dielectric material.
 16. The opticaltransmission grating of claim 1 wherein a transverse cross section ofeach ridge is substantially rectangular or substantially trapezoidal.17. A method for forming the optical transmission grating of claim 1,the method comprising: (i) forming a set of multiple, discrete,spaced-apart, elongated grooves at least partly through a layer of thesecond dielectric material layer, thereby forming the ridges of thesecond dielectric material; and (ii) depositing on the ridges andgrooves the third dielectric material to substantially fill the groovesand to cover the ridges to the thickness t₃, wherein: (iii) the seconddielectric material layer covers a layer of the first dielectricmaterial to the thickness t₂; and (iv) the first dielectric materiallayer covers the substrate to the thickness t₁.
 18. The method of claim17 further comprising forming the first dielectric material layer on thesubstrate and forming the second dielectric material layer on the firstdielectric material layer.